new laptop to share net connection with old desktop?

How do i (if possible) share my one internet connection with both my desktop and laptop? the desktop does not have wireless capability. can i plug it into the modem, along with the router? also they are using different OS. laptop has windows 7 and desktop has xp.
i have a router, and am on the net on the lap top. but my desk top is having connection issues. they can each access on their own but not at the same time. how do i fix that?
 
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